Abstract In this paper, we investigate the limit points set of essential spectrum of upper triangular operator matrices We prove that accσe(MC) ∪ W = accσe(A) ∪ accσe(B) where W is the union of certain holes in accσe(MC), which happen to be subsets of accσe(B) ∩ accσe(A). Also, several sufficient conditions for accσe(MC) = accσe(A) ∪ accσe(B) holds are given.

Abstract: In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices . We prove that σ*(MC) ∪ W=σ*(𝐴)∪σ*(𝐵) where W is the union of certain holes in σ*(MC), which happen to be subsets of σlgD(𝐵) ∩ σrgD(𝐴), σ* ∈ {σlgD, σrgD} are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ* (MC) = σ* (𝐴)∪σ* (𝐵) holds for every C ∈ ℬ(Y,X) are given.

Abstract In this paper a novel design of microstrip diplexer and triplexer using open loop resonators is presented. The proposed diplexer if formed by two band-pass filters for the Industrial Scientific Medical (ISM) applications at 5.8 GHz and the WIMAX applications (IEEE 802.16 WiMAX at 3.17 GHz to 4.2 GHz bands). The microstrip triplexer is designed for the Digital Communication System (DCS) at 1.8 GHz, WIMAX at 3.2 GHz and for the C-band at 4.4 GHz. Each device is formed by a set of filters with a matching network by using open loop resonators and a good arrangement of the transmission feed lines. Several parametric studies were achieved to study the influence of some critical parameters on the performances of the proposed circuits. The LC equivalent circuit of the band pass filter is examined and the values of its components are calculated. ADS Agilent and CST-MWS solvers are used to predict the electrical performances of the proposed circuits. The simulated frequency responses of these structures show good results with insertion losses around 2 dB, return losses better than 20 dB for all channels, and an isolation between all bands better than 20 dB. Besides, several transmission zeros are observed near the pass bands which enhance the selectivity and the isolation of the proposed devices.

In this paper, a new microstrip diplexer using open loop resonators with compact size and high isolation is designed and fabricated for the WLANs (IEEE 802.11b/g at 2.4 GHz and IEEE 802.11a at 5.2 GHz) applications. The diplexer is formed by two dual-mode band pass filters (BPFs) using an asymmetric fork-form feed line and two open loop resonators. The diplexer has less than 3 dB insertion loss and the isolation between the two channels is more than 25 dB. Furthermore, the proposed diplexer shows several transmission zeros beside the pass bands which improves the selectivity of the BPFs and thus improves the isolation between lower and upper channel filters and achieves a significant attenuation of the undesired harmonics. The electrical performances of the diplexer are investigated numerically by using Momentum integrated in ADS Agilent and CST microwave software. Good agreement between the simulation and measurement results is achieved.